Finite Group Databasebeta

← C2×#13082240 #15660875

Subgroups — C2×#13082240 #15660875

Order 2816.

8418 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082240C2132yesmaximal, direct product factor
2C2×#10623253C211yesmaximal, characteristic, complemented
3C2×#10623265C211yesmaximal, characteristic, complemented
4C2×#10623147C214yesmaximal, complemented
5C2×#10623201C214yesmaximal, complemented
6C2×#10623249C212yesmaximal, complemented
7C2×#10623130C214yesmaximal, complemented
8C2×#10623079C214yesmaximal, complemented
9C2×#10623363C214yesmaximal, complemented
10C2×C4×#4339C212yesmaximal, complemented
11C2×C4×#4341C214yesmaximal, complemented
12C2×C11×#532C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×#4341C2214yes—
15C22×#4339C2212yes—
16C22×#4339C2214yes—
17C11×#532C22116yescomplemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124C2212yes—
21C2×C11×#121C2214yes—
22C2×C4×D4×C11C2214yes—
23C22×C42×C11C2211yescharacteristic
24#10623363C22164yescomplemented
25C2×#67000C2214yes—
26C2×#66997C2214yes—
27C2×#66993C2214yes—
28C2×#66993C2214yes—
29C2×#66992C2218yes—
30C2×#66992C2218yes—
31C2×#66991C2214yes—
32C2×#66989C2214yes—
33C2×D4×Dic11C2214yes—
34C2×C4×C22⋊D11C2214yes—
35C2×C4×C22⋊D11C2218yes—
36C2×C4×C22⋊D11C2214yes—
37C2×#66979C2212yes—
38C22×C4×Dic11C2214yes—
39#10623265C22116yescomplemented
40#10623253C22116yescomplemented
41#10623249C22132yescomplemented
42#10623201C22164yescomplemented
43#10623147C22164yescomplemented
44#10623130C22164yescomplemented
45#10623079C22164yescomplemented
46C4×#4341C22164yescomplemented
47C2×#66948C2214yes—
48C2×#66945C2214yes—
49C2×#66941C2214yes—
50C2×#66940C2214yes—
51C2×#66938C2218yes—
52C2×#66937C2218yes—
53C2×(C22⋊D11)⋊C4C2218yes—
54C2×#66930C2218yes—
55C4×#4339C22132yescomplemented
56C2×C4×D44C2212yes—
57C2×C4×D44C2212yes—
58C2×#66925C2214yes—
59C2×C42×D11C2214yes—
60C2×C4×Dic22C2212yes—
61C2×C4×Dic22C2212yes—
62C2×C11×#41—48no—
63C2×C11×#41C23116yes—
64C22×Q8×C11C2312yes—
65C22×D4×C11C2314yes—
66C22×D4×C11C2314yes—
67C22×D4×C11C2312yes—
68C23×C4×C11C2314yes—
69C23×C4×C11C2312yes—
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11C2318yes—
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C2318yes—
74C23×Dic11C2318yes—
75C2×#4341—232no—
76C2×#4341C23132yes—
77C2×#4339—216no—
78C2×#4339—416no—
79C2×#4339C23116yes—
80C2×#4339C23132yes—
81C22×D44C2312yes—
82C22×D44C2314yes—
83C22×C4×D11C2314yes—
84C22×C4×D11C2314yes—
85C22×C4×D11C2314yes—
86C22×Dic22C2314yes—
87C22×Dic22C2312yes—
88C11×C4⋊Q8C2318yes—
89C11×#127C2318yes—
90C11×#124C23116yes—
91C11×#121C23132yes—
92C4×D4×C11C23132yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4C2318yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2318yes—
99C2×C22⋊Dic11C2318yes—
100C2×C22⋊Dic11C2314yes—
101#67000C23132yes—
102#66997C23132yes—
103#66993C23132yes—
104#66993C23132yes—
105#66992C23164yes—
106#66992C23164yes—
107#66991C23132yes—
108#66989C23132yes—
109D4×Dic11C23132yes—
110C4×C22⋊D11C23132yes—
111C4×C22⋊D11C23132yes—
112C4×C22⋊D11C23164yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2318yes—
116#66979C23116yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2318yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C23132yes—
128#66948C23132yes—
129#66945C23132yes—
130#66941C23132yes—
131#66940C23132yes—
132#66938C23164yes—
133#66937C23164yes—
134(C22⋊D11)⋊C4C23164yes—
135#66930C23164yes—
136C4×D44C23116yes—
137C4×D44C23116yes—
138#66925C23132yes—
139C42×D11C23132yes—
140C4×Dic22C23116yes—
141C4×Dic22C23116yes—
142C2×#3483—111nomaximal, Sylow
143C24×C11C2411yescharacteristic
144C24×C11C2414yes—
145C23×D11C2414yes—
146C11×#41—432no—
147C2×Q8×C11—44no—
148C2×Q8×C11C2418yes—
149C2×D4×C11—216no—
150C2×D4×C11—48no—
151C2×D4×C11—44no—
152C2×D4×C11C24116yes—
153C2×D4×C11C24116yes—
154C2×D4×C11C2418yes—
155C22×C4×C11—28no—
156C22×C4×C11—216no—
157C22×C4×C11—24no—
158C22×C4×C11C2412yes—
159C22×C4×C11C2414yes—
160C22×C4×C11C24116yes—
161C22×C4×C11C2411yescharacteristic
162C22×C4×C11C2418yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—216no—
167C2×C22⋊D11—232no—
168C2×C22⋊D11—416no—
169C2×C22⋊D11C24132yes—
170C2×C22⋊D11C24116yes—
171C2×C22⋊D11C24132yes—
172C22×Dic11—232no—
173C22×Dic11C24132yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C22×Dic11C2414yes—
177#4341—2128no—
178#4339—264no—
179#4339—464no—
180C2×D44—28no—
181C2×D44—48no—
182C2×D44C2418yes—
183C2×D44C24116yes—
184C2×C4×D11—216no—
185C2×C4×D11—216no—
186C2×C4×D11—216no—
187C2×C4×D11C24116yes—
188C2×C4×D11C24116yes—
189C2×C4×D11C24116yes—
190C2×Dic22—48no—
191C2×Dic22#41116yescomplemented
192C2×Dic22C24116yes—
193C2×Dic22C2418yes—
194C11×C4⋊C4C24116yes—
195C11×C22⋊C4C24132yes—
196C42×C11C2414yes—
197C42×C11C2418yes—
198C42×C11C2414yes—
199C22⋊Dic11C24132yes—
200C22⋊Dic11C24116yes—
201(C2×D11)⋊C4C24116yes—
202(C2×D11)⋊C4C24116yes—
203(C2×D11)⋊C4C24132yes—
204C4⋊Dic11C2418yes—
205C4⋊Dic11C2418yes—
206Dic11⋊C4C24116yes—
207Dic11⋊C4C24116yes—
208Dic11⋊C4C24132yes—
209C4×Dic11C24116yes—
210C4×Dic11C24116yes—
211C4×Dic11C24116yes—
212C4×Dic11C24116yes—
213C4×Dic11C24116yes—
214#3483—1132no—
215C2×Q82—111no—
216C2×#555—111no—
217C2×#555—114no—
218C2×#555—114no—
219C2×#550—112no—
220C2×#550—114no—
221C2×#532—114no—
222C2×#532—114no—
223C2×#532D1111yescharacteristic, complemented
224C2×C4×#41—112no—
225C2×C4×#41—114no—
226C23×C11—216no—
227C23×C11—24no—
228C23×C11—28no—
229C23×C11—22no—
230C23×C11C2512yes—
231C23×C11C2518yes—
232C23×C11C2511yescharacteristic
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—28no—
236C22×D11C2518yes—
237Q8×C11—48no—
238D4×C11—232no—
239D4×C11—48no—
240D4×C11—416no—
241C2×C4×C11—24no—
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—216no—
245C2×C4×C11—232no—
246C2×C4×C11—28no—
247C2×C4×C11C2×#4118yes—
248C2×C4×C11H(5,𝔽2)14yes—
249C2×C4×C11C2514yes—
250C2×C4×C11C2518yes—
251C2×C4×C11C2512yes—
252C2×C4×C11C2514yes—
253C2×C4×C11C2512yes—
254C22⋊D11—232no—
255C22⋊D11—264no—
256C22⋊D11—432no—
257C2×Dic11—28no—
258C2×Dic11—28no—
259C2×Dic11—264no—
260C2×Dic11C2×#41116yes—
261C2×Dic11C2518yes—
262C2×Dic11C2518yes—
263C2×Dic11C2518yes—
264D44—216no—
265D44—416no—
266C4×D11—232no—
267C4×D11—232no—
268C4×D11—232no—
269Dic22—416no—
270Dic22C2×#41132yescomplemented
271C22×#41—114no—
272C22×#41—112no—
273C22×#41—114no—
274C22×#41C2×D1112yes—
275Q82—1116no—
276#555—1116no—
277#555—1164no—
278#555—1164no—
279#550—1132no—
280#550—1164no—
281#532—1164no—
282#532—1164no—
283#532C2×D11116yescomplemented
284C2×C4⋊Q8—114no—
285C2×C4⋊Q8—114no—
286C2×C4⋊Q8C2×D1111yescharacteristic
287C2×#127—114no—
288C2×#127—114no—
289C2×#127C2×D1111yescharacteristic
290C2×#124—114no—
291C2×#124—114no—
292C2×#124—118no—
293C2×#124C2×D1112yes—
294C2×#121—114no—
295C2×#121—118no—
296C2×#121—118no—
297C2×#121—114no—
298C2×#121—118no—
299C2×#121C2×D1114yes—
300C4×#41—1164no—
301C4×#41—1132no—
302C2×C4×Q8—114no—
303C2×C4×Q8—112no—
304C2×C4×Q8—112no—
305C2×C4×D4—114no—
306C2×C4×D4—114no—
307C2×C4×D4—118no—
308C2×C4×D4—114no—
309C2×C4×D4—118no—
310C2×C4×D4—112no—
311C2×C4×D4—112no—
312C2×C4×D4C2×D1114yes—
313C2×#117—112no—
314C2×#117—114no—
315C2×#117—118no—
316C2×#117—114no—
317C22×C42—114no—
318C22×C42—114no—
319C22×C42C2×D1111yescharacteristic
320C22×C11—24no—
321C22×C11—216no—
322C22×C11—22no—
323C22×C11—28no—
324C22×C11—416no—
325C22×C11—44no—
326C22×C11C22×#4114yes—
327C22×C11C2×H(5,𝔽2)12yes—
328C22×C11C2611yescharacteristic
329C2×D11—28no—
330C2×D11—28no—
331C2×D11—28no—
332C2×D11—416no—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—28no—
336C4×C11C22×#4118yes—
337C4×C11C2×H(5,𝔽2)14yes—
338Dic11—28no—
339Dic11—28no—
340Dic11C22×#41116yes—
341C2×#41—48no—
342C2×#41—1132no—
343C2×#41—1116no—
344C2×#41—1132no—
345C2×#41—2216no—
346C2×#41—2232no—
347C2×#41—4416no—
348C2×#41C22×D11116yes—
349C22×Q8—112no—
350C22×Q8—114no—
351C22×Q8C22×D1112yes—
352C22×D4—114no—
353C22×D4—118no—
354C22×D4—118no—
355C22×D4—112no—
356C22×D4—114no—
357C22×D4C22×D1114yes—
358C22×D4C22×D1112yes—
359C22×D4C22×D1114yes—
360C23×C4—118no—
361C23×C4—114no—
362C23×C4—114no—
363C23×C4—114no—
364C23×C4C22×D1112yes—
365C23×C4C22×D1111yescharacteristic
366C23×C4C22×D1114yes—
367C4⋊Q8—1132no—
368C4⋊Q8—1132no—
369C4⋊Q8C22×D1118yes—
370#127—1132no—
371#127—1132no—
372#127C22×D1118yes—
373#124—1132no—
374#124—1132no—
375#124—1164no—
376#124C22×D11116yes—
377#121—1132no—
378#121—1164no—
379#121—1164no—
380#121—1132no—
381#121—1164no—
382#121C22×D11132yes—
383C4×Q8—1132no—
384C4×Q8—1116no—
385C4×Q8—1116no—
386C4×D4—1132no—
387C4×D4—1164no—
388C4×D4—1132no—
389C4×D4—1132no—
390C4×D4—1164no—
391C4×D4—1116no—
392C4×D4—1116no—
393C4×D4C22×D11132yes—
394#117—1116no—
395#117—1132no—
396#117—1164no—
397#117—1132no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—118no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4C22×D1114yes—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4C22×D1118yes—
410C2×C42—114no—
411C2×C42—114no—
412C2×C42—114no—
413C2×C42—114no—
414C2×C42—1132no—
415C2×C42—114no—
416C2×C42—1132no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1118yes—
420C2×C42C22×D1112yes—
421C2×C11—42no—
422C2×C11—48no—
423C2×C11#348314yescomplemented
424C2×C11C23×#4112yes—
425C2×C11C22×H(5,𝔽2)11yescharacteristic
426D11—48no—
427C24—114no—
428C24C23×D1111yescharacteristic
429C24C23×D1114yes—
430#41—432no—
431#41—2264no—
432#41—22128no—
433#41—4464no—
434C2×Q8—44no—
435C2×Q8—1116no—
436C2×Q8—118no—
437C2×Q8—1116no—
438C2×Q8—448no—
439C2×Q8C23×D1118yes—
440C2×D4—216no—
441C2×D4—44no—
442C2×D4—48no—
443C2×D4—1116no—
444C2×D4—1132no—
445C2×D4—1132no—
446C2×D4—118no—
447C2×D4—1116no—
448C2×D4—2216no—
449C2×D4—2232no—
450C2×D4—228no—
451C2×D4—448no—
452C2×D4—4416no—
453C2×D4C23×D11116yes—
454C2×D4C23×D1118yes—
455C2×D4C23×D11116yes—
456C22×C4—24no—
457C22×C4—216no—
458C22×C4—28no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—114no—
462C22×C4—1132no—
463C22×C4—1116no—
464C22×C4—1116no—
465C22×C4—1116no—
466C22×C4—2216no—
467C22×C4—2232no—
468C22×C4—2216no—
469C22×C4—2216no—
470C22×C4C23×D1112yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D11116yes—
473C22×C4C23×D1111yescharacteristic
474C22×C4C23×D1118yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1111yescharacteristic
478C4⋊C4—1116no—
479C4⋊C4—118no—
480C4⋊C4—1132no—
481C4⋊C4—1116no—
482C4⋊C4—118no—
483C4⋊C4C23×D11116yes—
484C22⋊C4—1116no—
485C22⋊C4—1132no—
486C22⋊C4—1132no—
487C22⋊C4—1116no—
488C22⋊C4—1116no—
489C22⋊C4C23×D11132yes—
490C42—1116no—
491C42—1116no—
492C42—1116no—
493C42—1116no—
494C42—1116no—
495C42C23×D1118yes—
496C42C23×D1114yes—
497C42C23×D1114yes—
498C11C2×#348311yescharacteristic, complemented, Sylow
499C23—22no—
500C23—28no—
501C23—24no—
502C23—216no—
503C23—118no—
504C23—228no—
505C23—228no—
506C23—228no—
507C23C24×D1112yes—
508C23C24×D1118yes—
509C23C24×D1111yescharacteristic
510Q8—48no—
511Q8—1132no—
512Q8—4416no—
513D4—232no—
514D4—48no—
515D4—416no—
516D4—2232no—
517D4—2264no—
518D4—2216no—
519D4—4416no—
520D4—4432no—
521C2×C4—22no—
522C2×C4—28no—
523C2×C4—24no—
524C2×C4—28no—
525C2×C4—232no—
526C2×C4—216no—
527C2×C4—1116no—
528C2×C4—118no—
529C2×C4—118no—
530C2×C4—118no—
531C2×C4—2232no—
532C2×C4—2264no—
533C2×C4—228no—
534C2×C4—228no—
535C2×C4—2232no—
536C2×C4—2232no—
537C2×C4#6703714yes—
538C2×C4#41×D1118yes—
539C2×C4C24×D1114yes—
540C2×C4C24×D1118yes—
541C2×C4C24×D1112yes—
542C2×C4C24×D1112yes—
543C2×C4C24×D1114yes—
544C22—24no—
545C22—216no—
546C22—22no—
547C22—28no—
548C22—44no—
549C22—416no—
550C22—228no—
551C22—228no—
552C22—228no—
553C22—4416no—
554C22C2×#6703712yes—
555C22C2×#41×D1114yes—
556C22C25×D1111yescharacteristic
557C4—24no—
558C4—22no—
559C4—28no—
560C4—1116no—
561C4—228no—
562C4—228no—
563C4C2×#6703714yes—
564C4C2×#41×D1118yes—
565C2—42no—
566C2—48no—
567C2—448no—
568C2#1308224014yesdirect product factor
569C2C22×#41×D1112yes—
570C2C22×#6703711yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#532C2
socleC23×C11C25
hypercenterC2×#532D11
hypocenterC11C2×#3483
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#532

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082240C2direct (N × H)
2. C2×#10623253C2semidirect
3. C2×#10623265C2semidirect
4. C2×#10623147C2semidirect
5. C2×#10623201C2semidirect
6. C2×#10623249C2semidirect
7. C2×#10623130C2semidirect
8. C2×#10623079C2semidirect
9. C2×#10623363C2semidirect
10. C2×C4×#4339C2semidirect
11. C2×C4×#4341C2semidirect
12. C2×C11×#532C2semidirect
17. C11×#532C22semidirect
24. #10623363C22semidirect
39. #10623265C22semidirect
40. #10623253C22semidirect
41. #10623249C22semidirect
42. #10623201C22semidirect
43. #10623147C22semidirect
44. #10623130C22semidirect
45. #10623079C22semidirect
46. C4×#4341C22semidirect
55. C4×#4339C22semidirect
191. C2×Dic22#41semidirect
223. C2×#532D11semidirect
270. Dic22C2×#41semidirect
283. #532C2×D11semidirect
423. C2×C11#3483semidirect
498. C11C2×#3483semidirect
568. C2#13082240direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130822402
C2×#106232532
C2×#106232652
C2×#106231472
C2×#106232012
C2×#106232492
C2×#106231302
C2×#106230792
C2×#106233632
C2×C4×#43392
C2×C4×#43412
C2×C11×#5322
C2×#348311